I have a 2003 Liberty Renegade with 105,000 miles on it. This problem with the idle started a long time again and still can't get any answers on how to fix it. It doesn't do it all the time, but when it does it is a pain in the butt. When I am just sitting there it will idle at 500rpms then all the sudden it will jump up to 1500 to 2000 and come back down. It also sounds like it is straining the engine to, like it is pulling to much power from it. I happens more often when I have the air conditioner or the defrosters on, but it will do it when they are not on too.

I have had the fuel system cleaned, spark plugs replaced. TPS sensor changed and some other stuff too. New battery installed too. I have taken it to 4 mechanics and nobody can figure it out.

Is your throttle body dirty/sticky? If so grab some cleaner and go through it as per directed on the cleaner.

Second, check your air filter for any rips/bent corners. I had this very same issue, noticed one corner of my k&n air filter was slightly bent changed it out for a normal paper one and boom fixed that issue.

Im no mechanic, but what you are explaining is exactly what happened to mine.